Around £35bn of savers’ money is invested in so-called “income” funds that are falling worryingly short of their income targets.

British funds that specialise in income-paying shares are required, by the fund trade body, to produce a yield that beats that of the FTSE All Share index by 10pc each year. Yields are calculated by setting dividend income against the value of a share or basket of shares, such as fund or index. Funds that fail to beat the stock market yield over a three-year period risk losing their “equity income” fund title.

Research for The Telegraph's Your Money conducted by Hargreaves Lansdown, the fund shop, found that more than half of the funds labelled “UK equity income” were failing to meet the requirement.

At present the FTSE All Share is yielding 3.43pc, so to beat the index by 10pc funds would need to produce a yield of more than 3.77pc. The yield figure is calculated as a 12-month average. As things stand today, 51 of the 96 UK equity income funds, which collectively manage £70bn of savers’ assets, are undershooting the yield target. As this is one of the most popular sectors for Isa and other investors, the suggestion is that many savers are unaware that their holdings are not living up to their name.

Adrian Lowcock of Hargreaves Lansdown said the data should serve as a note of caution for Isa savers relying on funds to supplement their earnings.

Income yields are falling on UK dividend-paying shares across a variety of sectors on the back of the London stock market’s strong performance in recent years. Over three years the index is up by 15pc to about 6500 this week.

Mr Lowcock said that, as the stock market climbed towards 7000, investors buying in today needed to accept that yields would continue to fall.

“Yields across the board are falling as a result of share price rises, but in many cases the actual dividend paid has risen,” he said. “So existing investors have got higher income but the yield looks lower because prices have risen. But for new investors the lower yields are a real headache as they are being forced to accept a much lower income than they would have got for their money a couple of years ago.”

Paul Surguy, who picks funds as part of his job as a portfolio manager for Sanlam Private Investments, said after a couple of record-breaking years in terms of dividend payouts from FTSE 100 companies, the vast majority of fund managers were hunting for value outside the index, instead buying small, up-and-coming British businesses, which had much lower yields.

Funds highlighted as having low yields included Standard Life Investments UK Equity High Income, Unicorn UK Income and River & Mercantile UK Equity Income. All three funds’ yields are around the 3pc mark. But over three years all three funds have been among the strongest performers in terms of “total return” – income plus capital growth. This suggests that these funds prioritise the latter over income. Some investors – those not depending on income – might be entirely satisfied with the results.

By contrast, the funds with high yields are what industry experts describe as “true” income funds. Funds that fall into this category typically sacrifice capital growth for dividend yield.

Experts argue that these funds are more suitable for savers looking to income funds to supplement their earnings. Those who are retired and seeking to add to their pension income may be better served by this type of income fund. Bear in mind that these high yields are not guaranteed.

However, savers with a longer time frame should focus on funds that have a track record for consistent growth in the income.

Brian Dennehy of the fund supermarket FundExpert.co.uk said: “For investors the key issue is payout growth in the long run. A yield of 5pc now is no use to an investor in 10 years’ time if the underlying payout hasn’t grown. Better to start with a yield of 4pc and consistently grow the payout every year, ideally by between 5pc and 10pc.”

This approach was echoed by other experts, including Paul Taylor of McCarthy Taylor, the independent financial adviser. But Mr Taylor also pointed out that low-yielding funds should be avoided, even if they were producing a stable income stream.

“Clearly if a UK income fund is yielding 3pc, even if it is generating income growth that is, say, 10pc a year, it is going to take a long time for investors to get a high level of income even if they are extremely patient and willing to hold the fund for several years,” he said.

Mr Dennehy added that over the past 10 years no fund had grown its dividend payments year in, year out. But a handful had increased payouts in nine of the past 10 years. His favourite income funds are Artemis Income and JO Hambro UK Equity Income.

In stark contrast, a handful of UK equity income investment trusts, which are similar to funds but listed on the London Stock Exchange, have managed to maintain or increase their divided payments each year since 2004. This has been mainly thanks to the fact that investment trusts can retain some of their income in reserve each year.

When the underlying investments struggle to generate enough income the company can dip into the reserves to avoid cutting payouts to its shareholders.

City of London and Temple Bar are two investment trusts with exemplary long-term track records for increasing income payments each year.